2. Selected examples 1. Anomalous skin depth in ICPs J.D. Evans and F.F. Chen, Phys. Rev. Lett. 86, 5502 (2001). 2. Anomalous transport in helicon discharges M. Light, F.F. Chen, and P.L. Colestock, UCLA LTP-101 (January, 2001). M. Light, F.F. Chen, and P.L. Colestock, Phys. Plasmas 8, 4675 (2001). M. Light, F.F. Chen, and P.L. Colestock, Plasma Sources Sci. Technol. 11, 273 (2002). 3. Parametric instabilities in helicon discharges J.L. Kline and E.E. Scime, Phys. Plasmas 10, 135 (2003). J.L. Kline et al., Phys. Plasmas 10, 2127 (2003). M. Krämer et al., Proc. EPS Conf. on Plasma Phys. and Control. Fusion, Montreux (2002) 26B, O4.08. B. Lorenz, M. Krämer, V.L. Selenin, and Yu.M. Aliev, Plasma Sources Sci. Technol. 14, ??? (2005). UCLA

3. Three types of ICPs* UCLA *ICP = Inductively Coupled Plasma

4. UCLA Density uniformity in a commercial ICP Data by John Evans

5. UCLA In the plane of the antenna, the density peaks well outside the classical skin layer Data by John Evans

6. Thermal diffusion of fast electrons UCLA

7. Consider the nonlinear effect of the Lorentz force on the motion of an electron in an RF field E  FLFL

8. An electron trajectory over four RF cycles with and without the Lorentz force F L

9. UCLA The electron's energy is large only inside the skin, if the Lorentz force is neglected

10. UCLA The effect of the Lorentz force is to push the electrons in the radial direction, causing them to bounce off the wall at a steep angle, so that they reach the central region before losing their energy in the next half cycle.

11. UCLA

14. Electron positions after 32,000 time steps

15. UCLA With no losses, the electron energy would just keep rising

16. UCLA Effects included in realistic calculations  Elastic and inelastic collisions with neutrals (w. probability at given p 0 and local electron velocity)  Losses through the wall sheath (prescribed sheath drop)  Regeneration of electrons at an arbitrary position with an arbitrary velocity according to a Maxwellian distribution at chosen KT e.  Exact skin layer field with collisions and cylindrical geometry included. Neglected: Motions and gradients in the z direction

17. UCLA 4000 points 2 MHz, 3E10, 10 mTorr, 3eV, 2.5 nsec, 20-V sheath

18. UCLA 32000 points

19. UCLA Density profile in four sectors of equal area Points are data from Slide 5

20. UCLA The number of ionizing electrons is largest in the central region

21. UCLA CONCLUSIONS 1. Ionizing electrons are created throughout the discharge, even outside the classical skin layer 2. This population must be treated kinetically, including the nonlinear Lorentz force. 3. Density tends to peak on axis because of the long residence time of slow electrons created there. 4. To achieve uniform density, IT IS NOT NECESSARY TO HAVE ANTENNA ELEMENTS NEAR THE AXIS!

22. The "standing wave" effect UCLA

23. A detached current layer UCLA

24. The field of a detached current ring UCLA

25. The "standing wave" effect UCLA

26. Selected examples 1. Anomalous skin depth in ICPs J.D. Evans and F.F. Chen, Phys. Rev. Lett. 86, 5502 (2001). 2. Anomalous transport in helicon discharges M. Light, F.F. Chen, and P.L. Colestock, UCLA LTP-101 (January, 2001). M. Light, F.F. Chen, and P.L. Colestock, Phys. Plasmas 8, 4675 (2001). M. Light, F.F. Chen, and P.L. Colestock, Plasma Sources Sci. Technol. 11, 273 (2002). G.R. Tynan et al, Plasma Phys. Control. Fusion 46, A373 (2004). 3. Parametric instabilities in helicon discharges J.L. Kline and E.E. Scime, Phys. Plasmas 10, 135 (2003). J.L. Kline et al., Phys. Plasmas 10, 2127 (2003). M. Krämer et al., Proc. EPS Conf. on Plasma Phys. and Control. Fusion, Montreux (2002) 26B, O4.08. B. Lorenz, M. Krämer, V.L. Selenin, and Yu.M. Aliev, Plasma Sources Sci. Technol. 14, ??? (2005). UCLA

27. Max Light's helicon source at LANL UCLA

28. Density vs. B 0 for various gases UCLA n(B 0 ) saturates or peaks at a critical field B crit that increases with ion mass. Linear theory predicts n to grow linearly with B 0.

29. Time Spectrum B 0 < B crit B 0 > B crit

30. Density saturates when instability starts UCLA It is a combined drift and Kelvin- Helmholtz instability

31. Diagnostics UCLA Triple probe for measuring ñ and Capacitance neutralization is used to float two probes for measuring potential oscillations. This is for getting the anomalous transport.

32. This is for neon. The onset agrees with the maximum theor. growth rate. But the radial flux stops at high B 0.

33. The radial transport stops before reaching the edge UCLA How does the plasma get out?

34. Axial ion flow with a Mach probe UCLA The plasma is oscillation-driven to the outside half, where it is then mainly lost by axial flow. This complicated loss mechanism is not entirely understood.

35. Similar effects were also seen by Tynan et al.* UCSD *J. George, Ph.D. Thesis, UCSD, G.R. Tynan et al, Plasma Phys. Control. Fusion 46, A373 (2004). M.J. Burin, G.R. Tynan, G.Y. Antar, N.A. Crocker, and C. Holland, Phys. Plasmas 12, 052320 (2005)

36. A region of large electric field shear UCSD

37. Fluctuations do not extend to radial wall UCSD

38. Selected examples 1. Anomalous skin depth in ICPs J.D. Evans and F.F. Chen, Phys. Rev. Lett. 86, 5502 (2001). 2. Anomalous transport in helicon discharges M. Light, F.F. Chen, and P.L. Colestock, UCLA LTP-101 (January, 2001). M. Light, F.F. Chen, and P.L. Colestock, Phys. Plasmas 8, 4675 (2001). M. Light, F.F. Chen, and P.L. Colestock, Plasma Sources Sci. Technol. 11, 273 (2002). 3. Parametric instabilities in helicon discharges J.L. Kline and E.E. Scime, Phys. Plasmas 10, 135 (2003). J.L. Kline et al., Phys. Plasmas 10, 2127 (2003). M. Krämer et al., Proc. EPS Conf. on Plasma Phys. and Control. Fusion, Montreux (2002) 26B, O4.08. B. Lorenz, M. Krämer, V.L. Selenin, and Yu.M. Aliev, Plasma Sources Sci. Technol. 14, ??? (2005). UCLA

39. Introduction to energy coupling in helicons UCLA

40. Scime's helicon machine at West Virginia UCLA J.L. Kline and E.E. Scime, Phys. Plasmas 10, 135 (2003). Detection of parametric instabilities in helicons

41. Fluctuation spectra downstream UCLA Electrostatic signalMagnetic signal f 0 = 11 MHz, f LH  9  MHz  f LF  1 MHz

42. Relation to the lower hybrid frequency UCLA k  ( ) and k z ( ) of LF wave Amplitudes of the lower and upper sideband waves LH Something happens just above the LH frequency

43. Other data UCLA The waves are located near the axis Amplitude of the sideband (  ) grows linearly with the pump ( ). This shows that the sideband is NOT from parametric decay.

44. Relation to anomalous ion T  's Power in LF wavePerpendicular ion temperature Parametric excitation of LH waves could cause the high ion T  's. This happens for pump frequency BELOW  LH at center, but near  LH at the edge.

45. Bottom line UCLA The Kline-Scime experiment was the first to detect daughter waves from some sort of parametric decay, but their interpretation of the data was probably wrong. A wave near the LH frequency was seen, but it did not fit into a parametric decay scheme.

46. Sidebands were seen in the VASIMR space thruster Pump: 25 MHz; gas: He The B-field was very non-uniform, so no definite conclusions were possible. Boswell, Sutherland, Charles, Squire, Chang-Diaz, Glover, Jacobson, Chavers, Bengtson, Bering, Goulding, and Light, Phys. Plasmas 11, 5125 (2004).

47. Decay into ion cyclotron waves UCLA Sutherland et al. saw EICW waves and explained them by a complicated 4-wave process involving filamenta- tion of the helicon pump. O. Sutherland, M. Giles, and R. Boswell, Phys. Rev. Lett. 94, 205002 (2005).

48. A more definitive experiment on parametric instabilities in helicon discharges UCLA Lorenz, Krämer, Selenin, and Aliev* used: 1. Test waves in a pre-formed plasma 2. An electrostatic probe array for ion oscillations 3. Capacitive probes for potential oscillations 4. Microwave backscatter on fluctuations 5. Correlation techniques to bring data out of noise *B. Lorenz, M. Krämer, V.L. Selenin, and Yu.M. Aliev, Plasma Sources Sci.Technol. 14 (2005).

49. Krämer's machine UCLA

50. A helicon wave at one instant of time UCLA Note that the scales are very different!

51. Damping rate in the helicon afterglow UCLA The damping rate increases with P rf, showing the existence of a nonlinear damping mechanism.

52. Excitation of a low-frequency wave UCLA The LF wave is larger with the e.s. probe than with the capacitive probe, showing that the wave is electrostatic. As P rf is raised, the sidebands get larger due to the growth of the LF wave.

53. Oscillations are localized in radius and B-field UCLA The fluctuation power and the helicon damping rate both increase nonlinearly with rf power.

54. Proposed parametric matching conditions UCLA k1k1 k2k2 k0k0 k 0 = helicon wave, k 1 = ion acoustic wave k 2 = Trivelpiece-Gould mode This was verified experimentally.

55. Evidence for m = 1 ion acoustic wave UCLA The cross phase between two azimuthal probes reverses on opposite sides of the plasma. k  is larger than k r, and both increase linearly with frequency. From the slope one can calculate the ion acoustic velocity, which yields T e = 2.8 eV, agreeing with 3 eV from probe measurements.

56. With a test pulse, the growth rate can be seen directly From probe data From  wave backscatter Growth rate vs. power

57. Conclusion on parametric instabilities UCLA Kramer et al. showed definitively that damping of helicon waves by parametric decay occurs near the axis. They identified the decay waves, checked the energy balance, and even checked the calculated instability threshold and growth rate. However, this process is too small to be the major source of energy transfer from the antenna to the plasma. It is still unknown what happens under the antenna, where it is difficult to measure. It could be that the waves observed were actually created under the antenna but measured downstream.

58. Conclusion on nonlinear effects in low- temperature plasma physics UCLA We have given three examples of interesting, fundamental plasma physics problems that occur in partially ionized plasmas. Connection is made with concepts learned from high-temperature, fusion-type plasmas. Low-temperature plasma physics does not have to be dirty science; there are clean, challenging problems to be solved.

59. Title here